Question

In B E C, F is the centroid, and AC = 12. Find A F and F C

Answer 1

bearing in mind that the centroid in a triangle cuts each of the three medians in a 2:1 ratio.

since we know that A C = 12, let's split it in a 2:1 ratio then, cleary from the picture the larger is F C, so F C : A F is on a 2:1 ratio.

$\bf A C=A F+F C\qquad \qquad \cfrac{F C}{A F}=\cfrac{2}{1}\qquad \qquad \cfrac{2\cdot \frac{12}{2+1}}{1\cdot \frac{12}{2+1}}\implies \cfrac{2\cdot 4}{1\cdot 4}\implies \cfrac{8}{4}$